1. Field of the Invention
The invention relates to a simulation method, a simulation program, and a simulator which simulate a change of a particle, a droplet, or a water-droplet over elapsed time.
2. Description of the Related Art
Conventionally, a numerical simulation is performed by a computer to analyze significantly complicated physical laws which rule natural phenomena such as a cloud formation, a rainfall, a snowfall, a thunderstrike, and so on. By virtue of improvement of analysis accuracy in the numerical simulation, natural phenomena which have actually occurred are accurately reproduced on a computer, and natural phenomena which are to occur in the future are accurately predicted.
In general, in such a numerical simulation, to analyze extremely complicated physical laws which rule the natural phenomena, the natural phenomena are grouped into two processes to be processed by a computer. One of the two processes is a cloud dynamics process which processes air flow while the other process is a cloud microphysics process which processes a movement and a change in a state of a water-droplet which constructs a cloud or rainfall. By the way, these processes influence each other.
A fluid dynamics model, which is a conventional method, is used to simulate the cloud dynamics process. In the simulation of the cloud dynamics process, calculation accuracy is swiftly improved by virtue of fast progresses in computer technologies.
On the other hand, in the simulation of the cloud microphysical process, a cloud is formed of a great number, such as approximately 109, of water-droplets per cubic meter. Therefore, in present and future, it is and will be impossible for a computer to exactly calculate all the cloud microphysics processes.
In view of the above, in present, a roughly approximated model is used to numerically simulate the cloud microphysics processes. Here, concerning to the simulation of the cloud microphysics processes, there will be specifically described conventional methods (an exact Monte Carlo method, an enhanced Monte Carlo method, a bin method, and a bulk parameterization method).
In the exact Monte Carlo method (see D. T. Gillespie, “An Exact Method for Numerically Simulating the Stochastic Coalescence Process in a Cloud”, J. Atoms. Sci., 32, 1977 (1975)), numeric values generated at random are used to simulate a probability of collision between water-droplets in a cloud. Thus, it is theoretically possible to accurately simulate the cloud microphysics processes. However, a great deal of data storage space and computational cost is required. The exact Monte Carlo method has been greatly improved (referred to as an “improved Monte Carlo method” hereafter, see M. See Belberg, T. Trautmann, and M. Thorn “Stochastic simulations as a benchmark for mathematical methods solving the coalescence equation”, Atmos. Res., 40, 33 (1996)”). The improved Monte Carlo method requires no huge data storage space but still a great deal of computational cost.
Here, description will be given, about an approximate computation time in the great deal of computational cost taken by the exact Monte Carlo method and the improved Monte Carlo method. According to “Stochastic simulations as a benchmark for mathematical methods solving the coalescence equation”, a computer at that time took 5.5 hours to simulate phenomena in a space of 50 [m3] for 20 minutes.
Accordingly, assuming that phenomena in a space of at least approximately 103 [km3]=1012 [m3] needs to be simulated for approximately two hours to calculate phenomena of a cloud formation and precipitation, the computer takes 6.6×1011 hours=7.5×107 years. Performance of a computer is supposed to continue to be improved by 100 times faster per 10 years. Then, the computer will be able to simulate the phenomena at a reasonable computational cost as long as 50 years later.
In the bin method (see A. Bott, “A Flux Method for the Numerical Solution of the Stochastic Collection Equation”, J. Atoms. Sci., 55, 2284 (1998) and A. Bott, “A Flux Method for the Numerical Solution of the Stochastic Collection Equation: Extension to Two-Dimensional Particle Distributions”, J. Atoms. Sci., 57, 284 (2000)), the water-droplets in a space where a cloud is formed are processed not individually but as a distribution function. Thus, the water-droplets are modeled into a bin model in which different distribution functions are obtained corresponding to different attributes (properties) of the water-droplets for calculation. Concerning to the bin method, the present computer can numerically simulate the microphysics processes of the cloud formation in a sufficient scale. In the bin method, since the water-droplets are not individually processed, it is not always possible to accurately express phenomena caused by a particulate property of the water-droplets.
Moreover, in the bin method, the water-droplets are processed as a distribution function. Therefore, to improve accuracy in the present bin model and increase the number of attributes of the water-droplets, it is expected to require a higher dimensional distribution function and more huge computational cost and data storage space. Assuming that the attributes of the water-droplet include only a radius R[m] of the water-droplet, merely one-dimensional distribution function is required for the simulation. By the way, the distribution function is a number density distribution function f(R), for instance. Here, f(R)dR is defined as the number of water-droplets which have a radius between R and R+dR.
Next, a case will be described, in which a plurality of attributes of the water-droplet are processed using the bin method to further improve accuracy in the simulation. For instance, there are assumed to be seven attributes including the radius R of the water-droplet, a velocity of the water-droplet (three elements in x, y, and z directions), a mass of a cloud condensation nucleus such as NaCl dissolved in the water-droplet, a temperature of the water-droplet, and an electricity charged in the water-droplet. In the bin method, in theory, when the number of attributes is increased to 7, a 7-dimensional distribution function needs to be processed. Processing the 7-dimensional distribution function requires 6th power of the data storage space and 12th power of computation time as compared with a case of processing the one-dimensional distribution function.
In general, in the bin method, a d-th dimensional distribution function is assumed to be processed. Then, a micro-scale parameter proportional to a width of a bin for each dimension of the distribution function is defined as ε. The micro-scale parameter ε expresses how accurate the simulation is. The smaller the value of the micro-scale parameter ε is, the more accurate the simulation is. Thus, in the bin method, a required size of the data storage area is proportional to (1/ε)d while a required computation time is proportional to (1/ε)2d. As a result, the computation time dramatically increases as the dimension d of the distribution function increases so that it is expected that the simulation becomes difficult. In addition, in the bin method, in a case of processing not only a water-droplet in a liquid phase but also a snow, a hail, and so on in a solid phase, the number of attributes further increases so as to make the simulation even more difficult.
Presently, the bulk parameterization method (see E. Kessler, “On the Distribution and Continuity of Water Substance in Atmospheric Circulations”, Met. Monograph, Vol. 10, No. 32, American Meteorological Society, Boston, 84 pp and M. Murakami, “Numerical Modeling of Dynamical and Microphysical Evolution of an Isolated Convective Cloud”, J. Meteor. Soc. Japan, 68, 107 (1990)) is a mainstream method in which the cloud dynamics process is combined with the cloud microphysics process to simulate natural phenomena such as a cloud formation and a rainfall. The bulk parameterization method is characterized in greatly simplified parameters which expresses the cloud microphysics process. The parameters are adjusted to approximately reproduce the phenomena. Thus, the cloud microphysics process is incorporated into the cloud dynamics process. Therefore, it is impossible to directly calculate changes in a state of the cloud using the bulk parameterization method. Consequently, it is impossible to predict with high accuracy the natural phenomena (unpredictable weather conditions) which variously change.
As described above, how to process the cloud microphysics process is one of important issues in researches of meteorology and climatology. Moreover, a method (see B. H. Lynn, et al., “Spectral (Bin) Microphysics Coupled with a Mesoscale Model (MM5). Part I: Model Description and First Results”, Mon. Wea. Rev., 133, 44 (2005)) is being examined, in which the cloud microphysics process modeled by the bin method is coupled with the cloud dynamics process.
However, there are problems respectively in the above-described techniques. To be concrete, in the exact Monte Carlo method and the improved Monte Carlo method, there is a problem that too long time is taken for computation. In the bin method, there are a lot of problems such as inaccuracy due to the water-droplets processed as the distribution function, difficulty of enhancement due to computation time which dramatically increases as the number of attributes increases, and so on. In the bulk parameterization method, the cloud microphysics process is greatly simplified so that the computation time can be reduced. However, there is a problem that it is impossible to predict with high accuracy the natural phenomena (unpredictable weather conditions) which variously change.
In view of the above, it is an object of the present invention to provide a simulation method, a simulation program, and a simulator which solve the above-described problems, reduce computation time, prevent the computation time from increasing even when the number of attributes of the object increases, without processing an object including a water-droplet as a distribution function, and predict various natural phenomena with high accuracy.